Q19. By which smallest number must 5400
be multiplied to make it a perfect cube?
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1
Answer:
Smallest number that should be multiplied with 5400 to obtain a perfect cube is 5
Step-by-step explanation:
By prime factorisation of 5400, We get
5400 = 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5
When we group the factors by 3, We get
5400 = 2³ × 3³ × 5²
Clearly the last group has only 2 similar factors. And the missing one is an extra 5, so that the group of 3 is complete.
So the smallest number that should be multiplied with 5400 to obtain a perfect cube = 5.
5 × 5400 = 27000
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